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<h1 class="ltx_title ltx_title_section">Centroid of local neighborhood</h1>

<div id="Sx1.p1" class="ltx_para">
<p class="ltx_p">Calculation of the centroid in a local image neighborhood is a very
fast method for sub-pixel molecule localization and is used in <cite class="ltx_cite">[<a href="#bib.bib9" title="QuickPALM: 3D real-time photoactivation nanoscopy image processing in ImageJ" class="ltx_ref">1</a>]</cite>.
The algorithm does not estimate the intensity or imaged size of molecules,
and is sensitive to noise. The main idea is simply to calculate the
mean pixel positions weighted by the intensity of the image data.
The sub-pixel refinement of the coordinates is calculated as</p>
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<td class="ltx_align_center"><img id="Sx1.Ex1.m1" class="ltx_Math" style="vertical-align:-24px" src="mi/mi20.png" width="378" height="56" alt="\hat{x}_{0}=\frac{\sum_{x,y\in\mathcal{D}}{x\tilde{I}\left(x_{,}y\right)}}{%
\sum_{x,y\in\mathcal{D}}{\tilde{I}\left(x_{,}y\right)}}\,,\quad\hat{y}_{0}=%
\frac{\sum_{x,y\in\mathcal{D}}{y\tilde{I}\left(x,y\right)}}{\sum_{x,y\in%
\mathcal{D}}{\tilde{I}\left(x,y\right)}}\,."></td>
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<h2 class="ltx_title ltx_title_subsection">See also</h2>

<div id="Sx1.SSx1.p1" class="ltx_para">
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<li id="I1.i1" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I1.i1.p1" class="ltx_para">
<p class="ltx_p"><a href="Estimators.html" title="" class="ltx_ref">Sub-pixel 2D localization of molecules</a></p>
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</li>
<li id="I1.i2" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I1.i2.p1" class="ltx_para">
<p class="ltx_p"><a href="FittingRegion.html" title="" class="ltx_ref">Definition of the fitting region</a></p>
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<div id="bib" class="ltx_bibliography">
<h1 class="ltx_title ltx_title_bibliography">References</h1>

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<li id="bib.bib9" class="ltx_bibitem ltx_bib_article">
<span class="ltx_bibtag ltx_bib_key ltx_role_refnum">[1]</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_author">R. Henriques, M. Lelek, E. F. Fornasiero, F. Valtorta, C. Zimmer and M. M. Mhlanga</span><span class="ltx_text ltx_bib_year">(2010)</span>
</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_title">QuickPALM: 3D real-time photoactivation nanoscopy image processing in ImageJ</span>,
</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_journal">Nature Methods</span> <span class="ltx_text ltx_bib_volume">7</span> (<span class="ltx_text ltx_bib_number">5</span>), <span class="ltx_text ltx_bib_pages"> pp. 339–340</span>.
</span>
<span class="ltx_bibblock">External Links: <span class="ltx_text ltx_bib_links"><a href="http://dx.doi.org/10.1038/nmeth0510-339" title="" class="ltx_ref doi ltx_bib_external">Document</a></span>.
</span>
<span class="ltx_bibblock ltx_bib_cited">Cited by: <a href="#Sx1.p1" title="Centroid of local neighborhood" class="ltx_ref"><span class="ltx_text ltx_ref_title">Centroid of local neighborhood</span></a>.
</span>
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